# mixed effects model

This is Part 1 of a two part lesson. Mixed-effects models, however, recognize correlations within sample subgroups. When to Use? Lastly, the course goes over repeated-measures analysis as a special case of mixed-effect modeling. Some doctors’ patients may have a greater probability of recovery, and others may have a lower probability, even after we have accounted for the doctors’ experience and other meas… The within-group errors are allowed to be correlatedand/or have unequal variances. When to choose mixed-effects models, how to determine fixed effects vs. random effects, and nested vs. crossed sampling designs. In a linear mixed-effects model, responses from a subject are thought to be the sum (linear) of so-called fixed and random effects. Practical example: Logistic Mixed Effects Model with Interaction Term Daniel Lüdecke 2020-12-14. causing a main effect/interaction) and random (i.e. - Subjects’ slope will vary by pizza consumption intercepts, and by timepoint intercepts. In this case would need to be consider a cluster and the model would need to take this clustering into … In summary, we have seen how two schools of thought treat fixed and random effects, discussed when to use fixed effects and when to use random effects in both frameworks, discussed the assumptions behind the models, and seen how to implement a mixed effect model in R. Fixed and random effect models still remain a bit mysterious, but I hope that this discussion cleared up a few … Therefore, using a mixed model allows you to systematically account for item-level variability (within subjects) and subject-level variability (within groups). The random effects have prior distributions, whereas the fixed … Nathaniel E. Helwig (U of Minnesota) Linear Mixed-Effects Regression Updated 04-Jan-2017 : Slide 9 This function can work with unbalanced designs: This function can work with unbalanced designs: lme1 = lme(yield ~ nf + bv * topo, random= ~1|rep, data=dat) 0000000596 00000 n Below are some important terms to know for understanding the statistical concepts used in mixed models: Crossed designs refer to the within-subject variables (i.e. no clustering. In addition to patients, there may also be random variability across the doctors of those patients. Random effects are random variables in the population Typically assume that random effects are zero-mean Gaussian Typically want to estimate the variance parameter(s) Models with ﬁxed and random effects are calledmixed-effects models. Hypotheses For Study Random effects: - “Subjects” will have their own intercepts. Random intercepts models, where all responses in a group are additively shifted by a value that is specific to … Mathematically, mixed-effects models can be seen as a hierarchical system of regression equations where L1 parameters are function of the L2 equations. As with all regression models, their purpose is to describe a response variable as a function of the predictor variables. With mixed models we’ve been thinking of coefficients as coming from a distribution (normal). The effects are conditional on other predictors and group membership, which … Sometimes mixed-effects models are expressed as multilevel regression models (first level and grouping level models) that are fit simultaneously. Pizza study: The fixed effects are PIZZA consumption and TIME, because we’re interested in the effect of pizza consumption on MOOD, and if this effect varies over TIME. An interactive version with Jupyter notebook is available here. Some specific linear mixed effects models are. For example, an outcome may be measured more than once on the same person (repeated measures taken over time). Check estimates for beta value – time has a significant effect, improvement in mood by about 1 point over time. Value. Linear Mixed Effects models are used for regression analyses involving dependent data. A revolution is taking place in the statistical analysis of psychological studies. ")����46�[l6�����t cj��"�ݑ�,�-�{9Z���NB��A���}[1���0��W�qG�x��+Ƴq9Q���Jx�J� ��7 #�ֱ)�S���Z ��h�H^F��e��lN��PK��"��ʓʎ�{���qC=��TgGEM*ٶ�1��Q��D�乕�үiGS��qe>���WwL�K&���ʀ4��J6 3M���Y���p?�h^���8�G��0�m��yF�P�0�c�F����G�/�\$TZn,]0E�/�EfRL�. Check correlation of fixed effects – if too high, this may imply. Be able to make figures to … In a within subjects design, one participant provides multiple data points and those data will correlate with one … Generalized linear mixed-effects models allow you to model more kinds of data, including binary responses and count data. Sushmita Shrikanth. the names of the variables, as character vector in the terms-argument. %PDF-1.4 %���� A mixed effects model has both random and fixed effects while a standard linear regression model has only fixed effects. Mixed-effects models, however, recognize correlations within sample subgroups. Random-effects terms are associated with individual experimental units drawn at random from a population, and account for variations between groups that might affect the response. 14 answers. The core of mixed models is that they incorporatefixed and random effects. Summary. In this way, they provide a compromise between ignoring data groups entirely and fitting each group with a separate model. You should … When building your models, you can treat your predictor as a fixed & random factor. Chapter 17: Mixed Effects Modeling. 0 Or maybe multiple fields each contain … A revolution is taking place in the statistical analysis of psychological studies. A fixed effect is a parameterthat does not vary. A single measure of residual variance can’t account for both. <<050702A324ECEC43A1F0A889E3B500B8>]>> Psychology Definition of MIXED-EFFECTS MODEL: is used in the evaluation of variance where an experimenter assumes one or more variables as fixed and any further variables as random. Sometimes mixed-effects models are expressed as multilevel regression models (first level and grouping level models) that are fit simultaneously. Refer to the p-values in the output to see whether there was an improvement in fit. The researcher has 4 fields where they can collect data. Fixed effects are, essentially, your predictor variables. In addition to students, there may be random variability from the teachers of those students. For these models we do not need to worry about the assumptions from previous models, since these are very robust against all of them. A mixed model is similar in many ways to a linear model. We use the InstEval data set from the popular lme4 R package (Bates, Mächler, Bolker, & Walker, 2015). Mixed Effects Model can be used to model both linear and nonlinear relationships between dependent and independent variables. Thus, if you hold everything constant, the change in probability of the outcome over different values of your predictor of interest are only true when all covariates are held constant and you are in the same group, or a group with the same random effect. For example, a … All participants are providing multiple measurements. The null model will be fit to the maximal likelihood estimate. This concludes the tutorial on mixed effects models. While being connected to the internet, open R and type in: install.packages(“lme4”) Select a server close to you. If you are willing to assume that all the children have the same slope and intercept relating age to height then you can fit a regular linear … 0000001225 00000 n To fit a mixed-effects model we are going to use the function lme from the package nlme. The researcher uses a mixed effects model to evaluate fixed and random effects together. The core of mixed models is that they incorporate fixed and random effects. A random-intercepts model would adequately capture the two sources of variability mentioned above: the inter-subject variability in overall mean RT in the parameter $${\tau_{00}}^2$$, and the trial-by-trial variability in the parameter $$\sigma^2$$. NOTE - Predictor variables can be both fixed (i.e. It estimates the effects of one or more explanatory variables on a response variable. 0000002334 00000 n Intercepts: The baseline relationship between IV & DV. The effects package should also include p-values in the output. It is a data set of instructor evaluation ratings, where the inputs (covariates) include categories such as students and departments, and our response variable of interest is the instructor evaluation rating. To cover some frequently asked questions by users, we’ll fit a mixed model, inlcuding an interaction term and a quadratic resp. However, in mixed effects logistic models, the random effects also bear on the results. Linear Mixed Effects Models¶ Linear Mixed Effects models are used for regression analyses involving dependent data. This vignette demonstrate how to use ggeffects to compute and plot marginal effects of a logistic regression model. X is an n -by- p fixed-effects design matrix. Mixed-effects models might include factors that are not necessarily multilevel or hierarchical, for example crossed factors. Some technical detail: We can actually get the correct p-value for the mixed effects model from the above fixed effects model output. Each participant provided an average number of pizzas consumed, and measurements are collected at 15 timepoints. no clustering. Each data point consists of inputs of varying type—categorized into groups—and a real-valued output. effects model!! With linear mixed effects models, we wish to model a linear relationship for data points with inputs of varying type, categorized into subgroups, and associated to a real-valued output. This is the effect you are interested in after accounting for random variability (hence, fixed). Mixed-effect linear models Whereas the classic linear model with n observational units and p predictors has the vectorized form with the predictor matrix , the vector of p + 1 coefficient estimates and the n -long vectors of the response and the residuals , LMMs additionally accomodate separate variance components modelled with a set of random effects , Pizza Study: Different baseline levels of pizza consumption across subjects, Pizza study: The strength of the relationship between pizza consumption and mood will vary from person to person, resulting in random slopes per subject. 63 0 obj <>stream The ANOVA function allows you to compute Chi-squares between each model to see the improvement in model fit. 1Background Information. We use the InstEval data set from the popular lme4 R package (Bates, Mächler, … The subjects are sampled from … A linear mixed effects model is a hierarchical model: it shares statistical strength across groups in order to improve inferences about any individual … Definition. In a linear mixed-effects model, responses from a subject are thought to be the sum (linear) of so-called fixed and random effects. Crossed designs occur when multiple measurements are associated with multiple grouping variables. Mixed effects models are hierarchical in that they posit distributions for latent, unobserved parameters, but they are typically not fully Bayesian because the top-level hyperparameters will not be given proper priors. Generic functions such as print, plot and summary have methods to show the results of the fit. Mixed-effects models for binary outcomes have been used, for example, to analyze the effectiveness of toenail infection treatments (Lesaffre and Spiessens2001) and to model union membership of young males (Vella and Verbeek1998). While we have what we are calling ‘fixed’ effects, the distinguishing feature of the mixed model is the addition of this random component. For example, a … Mixed Models – Repeated Measures Introduction This specialized Mixed Models procedure analyzes results from repeated measures designs in which the outcome (response) is continuous and measured at fixed time points. Mixed effects models A mixed model is a good choice here: it will allow us to use all the data we have (higher sample size) and account for the correlations between data coming from the … As you can see by the p-values, while there is an improvement in fit from model 1 to model 2, model 3 did not explain more variance. Mixed-effects models are also called multilevel models or hierarchical models depending on the context. The list of random effects implemented in INLA is quite rich. Note. 0000002636 00000 n Note: If 2 variables share a lot of variance, the random intercepts and slopes may be correlated with one another. 0000048443 00000 n The following example will illustrate the logic behind mixed effects models. A O indicates the variable has a fixed intercept and not a random one. Because there was an improvement in between model 1 and model 2, but NO improvement between model 2 and model 3, we can proceed using the best fit model, nullmodel2, as our random effects structure for the rest of the analyses. 0000002369 00000 n Mixed effects models—whether linear or generalized linear—are different in that there is more than one source of random variability in the data. As with all regression models, their purpose is to describe a response variable as a function of the predictor variables. In today’s lesson we’ll learn about linear mixed effects models (LMEM), which give us the power to account for multiple types of effects in a single model. These are a few hypothetical random effects structures: The lmer package can be used for modeling, and the general syntax is as follows:  modelname <- lmer (dv ~ 1 + IV +(randomeffects), data = data.name, REML = FALSE). - Expecting interaction such that more pizza over time predicts mood. In this example given below, the patients’ response to the vaccine is modelled as the probability of the vaccinated person falling sick due to Covid-19. Some specific linear mixed effects models are. Mixed effects, or simply mixed, models generally refer to a mixture of fixed and random effects. Psychology Definition of MIXED-EFFECTS MODEL: is used in the evaluation of variance where an experimenter assumes one or more variables as fixed and any further variables as random. Generalized linear mixed-effects models allow you to model more kinds of data, including binary responses and count data. A model that contains both fixed and random effects is called a mixed model. This kind of data appears when subjects are followed over time and measurements are collected at intervals. Mixed-effects models account for both fixed and random effects. For example, we may assume there is some true regression line in the population, $$\beta$$, and we get some estimate of it, $$\hat{\beta}$$. β is a p -by-1 fixed-effects vector. Linear Mixed Effects Models in R - Which is the better approach to build and compare models? Logistic Mixed Effects Model with Interaction Term. b is a q -by-1 random-effects vector. By the end of this lesson you will: Have learned the math of an LMEM. Dependent Variable: Purchase made (Yes/No) Independent Variable 1: Time spent (in store or on website) Note: (Data contain repeated measures over time for consumers) The null hypothesis, which is statistical lingo for what would happen if the treatment does nothing, is that there is no relationship between time spent and whether or not a purchase is made. an object of class nlme representing the nonlinear mixed-effects model fit. Let’s understand how the patients’ response can be estimated using both fixed effects model, and, mixed model which combines both fixed and the random effects. Mixed Models and Random Effect Models. m2 <-glmer (outcome ~ var_binom * var_cont + (1 | group), data = dat, family = binomial (link = "logit")) To compute or plot marginal effects of interaction terms, simply specify these terms, i.e. We are going to work in lme4, so load the package … Mixed-effects models might include factors that are not necessarily multilevel or hierarchical, for example crossed factors. 0000000884 00000 n Hence, the p-value of machine is given by. 0000007707 00000 n Consider a case where you have data on several children where you have their age and height at different time points and you want to use age to predict height. A mixed-effects model consists of fixed-effects and random-effects terms. Such data arise when working with longitudinal and other study designs in which multiple observations are made on each subject. Random intercepts: Variability in baseline measurements, Fixed intercepts: Baseline variance is not affected. Although it has many uses, the mixed command is most commonly used for running linear mixed effects models (i.e., models that have both fixed and random effects). Keep REML = FALSE. Next, we fit a model with an interaction between the binomial and continuous variable. This generic function fits a nonlinear mixed-effects model in theformulation described in Lindstrom and Bates (1990) but allowing for nestedrandom effects. Specific predictors can now be introduced into our model by specifying the DV followed by the predictor, random effects, and the dataframe. 3.3 Types of mixed-effects models. We will also estimate fewer parameters and avoid problems with multiple comparisons that we would encounter while using separate regressions. Nested designs refer to the between-subject variable. If an effect is associated with a sampling procedure (e.g., subject effect), it is random. In a mixed-effects model, random effects contribute only to the covariance structure of the data. Linear Mixed Effects Models. A random effect model is a model all of whose factors represent random effects. The random effects structure reflects YOUR understanding of where to expect variance, and how nested data will interact with that variance. Do they interact? SD reflects the amount of variation. When we do that we have to account for both within-person and across-person variability. Mixed-Effects … spline term. A fixed effect is a parameter that does not vary. The data set denotes: 1. students as s 2. instructors as d 3. departments as dept 4. service as service If we divide the machine mean square by the mean square of the interaction effect we get 20.58. timepoint, condition, etc.). We demonstrate with an example in Edward. A further mixed-effects model is applied to the three WER components SUB, DEL and INS to evaluate how they affect the two systems. Nathaniel E. Helwig (U of Minnesota) Linear Mixed-Effects Regression Updated 04-Jan-2017 : Slide 9 trailer Now consider a standard regression model, i.e. Random effects in INLA are defined using a multivariate Gaussian distribution with zero mean and precision matrix $$\tau \Sigma$$, where $$\tau$$ is a generic precision parameter and $$\Sigma$$ is a matrix that defines the dependence structure of the random effects and that may depend on further parameters. Because the purpose of this workshop is to show the use of the mixed command, rather than to teach about multilevel models in general, many topics important to multilevel modeling will be mentioned but not discussed in … A mixed model is similar in many ways to a linear model. Generally this is a higher-level variable that subjects or items are grouped under. Slope: The strength of the relationship between IV & DV (controlling for randomness), which represent random effects. This is exctly the value as in the output of the mixed model from above … Mixed models are especially useful when working with a within-subjects design because it works around the ANOVA assumption that data points are independent of one another. Mixed effects models are useful when we have data with more than one source of random variability. Because subjects start at. Random effects are best defined as noise in your data. The function does not do any scaling internally: the … These are effects that arise from uncontrollable variability within the sample. The Mixed Modeling framework can specify a variety of model types including random coefficients models, hierarchical linear models, variance components models, nested models, and split-plot designs. Throughout the course you'll work with real data to answer … Here is some hypothetical data (code used to generate data can be found here): NOTE - This is a within-subjects study. In a completely crossed design, all subjects provide responses for all conditions/time-points. Linear Mixed-Effects Models y is the n -by-1 response vector, and n is the number of observations. For example, for unbalanced design with blocking, probably these methods … For example, assume we have a dataset where again we are trying to model yield as a function of nitrogen level. You can name each model whatever you want, but note that the name of the dataframe containing your data is specified in each model. This framework is widely applicable across numerous fields within the … Mixed models in R For a start, we need to install the R package lme4 (Bates, Maechler & Bolker, 2012). This class of models are used to account for more than one source of random variation. For example, in the above example we would most likely treat the mean income in a given ZIP as a sample from a normal distribution, with unknown mean and sigma to be estimated by the mixed … 0000005014 00000 n Random effects are factors whose levels were sampled randomly from a larger population about which we wish to generalize, but whose specific level values we actually don't care about. To better understand slopes and intercepts it maybe helpful to imagine plotting the relationship between the IVs and DV for each subject. 0000002185 00000 n A mixed model is a good choice here: it will allow us to use all the data we have (higher sample size) and account for the correlations between data coming from the sites and mountain ranges. For the models in general, I prefer the terms ‘mixed models’ or ‘random effects … 0000002885 00000 n Mixed-effects models is a more general term than the latter two. Mixed-effects models is a more general term than the latter two. - The slopes and intercepts of pizza consumption and time will be correlated (shared variance) Fixed effects: - Expecting there to be an overall main effect of pizza consumption over time. We can now conclude that after controlling for random effects, more pizza consumption does lead to improvements in mood over time, but there is no interaction with time. With mixed models we’ve been thinking of coefficients as coming from a distribution (normal). As such, model 2 appears to be the best fit. %%EOF Linear Mixed-Effects Models. This can be accounted for in random structures as well. In summary, we have seen how two schools of thought treat fixed and random effects, discussed when to use fixed effects and when to use random effects in both frameworks, discussed the assumptions behind the models, and seen how to implement a mixed effect model in R. Fixed and random effect models still remain a bit mysterious, but I hope that this discussion cleared … That is why mixed-effects is the terminology preferred here. However, this time the data were collected in many different farms. The general syntax is as follows: When there is a 1 before the line, you are accounting for random intercepts (varying baseline levels) in your variable. You should expect to see differences in the slopes of your random factors. Data. They are also common in scientific experiments where a given effect is assumed to be present among all study individuals which needs to be teased out from a … Thus, we have a crossed design. I’ll be taking for granted some of the set-up steps from Lesson 1, so if you haven’t done that yet be sure to go back and do it. w�00�ng ���� ��A� �� p1 In contrast, random effects are parameters that are themselves random variables. We can calculate the … The presence of … Random effects have a a very special meaning and allow us to use linear mixed in general as linear mixed models. … The following equations represent a two-level model with one L1 predictor, X , and one L2 predictor, W . Create a basic mixed-effects model: I’m not going to walk through the steps to building models (at least not yet), but rather just show an example of a model with coral cover as the response variable (elkhorn_LAI), herbivore populations & depth as fixed effects (c.urchinden, c.fishmass, c.maxD), and survey site as a random effect (site).. To illustrate the use of mixed model approaches for analyzing repeated measures, we’ll examine a data set from Landau and Everitt’s 2004 book, “A Handbook of Statistical Analyses using SPSS”. endstream endobj 50 0 obj <> endobj 51 0 obj <>/Font<>/ProcSet[/PDF/Text]/ExtGState<>>>/Type/Page>> endobj 52 0 obj <> endobj 53 0 obj <> endobj 54 0 obj <> endobj 55 0 obj [/ICCBased 60 0 R] endobj 56 0 obj <> endobj 57 0 obj <> endobj 58 0 obj <> endobj 59 0 obj <>stream Mixed Effects Model can be used to model both linear and nonlinear relationships between dependent and independent variables. It estimates the effects of one or more explanatory variables on a response variable. Results show significant effects of both pizza consumption and time on mood! Z is an n -by- q random-effects design matrix. Is a mixed model right for your needs? If an effect, such as a medical treatment, affects the population mean, it is fixed. First, however, we need to specify the random effects term that best fits the data. Nonlinear mixed-effects models are applied in many fields including medicine, public health, pharmacology, and ecology. Mixed Effects Logistic Regression Example. 0000001774 00000 n If some models are livestock and some are pets, this model is my dearest pet. Subject level variability is often a random effect. Model 2 – Pizza consumption and timepoints included as predictors of mood. if intercept increases, slope increases). While we have what we are calling ‘fixed’ effects, the distinguishing feature of the mixed model is the addition of this random component. Ordered outcomes have been studied by, for The functions resid, coef, fitted, fixed.effects, and random.effects can be used to extract some of its components. So, in interaction design and HCI studies, subject is a classic random effect. 0000000986 00000 n However, the researcher wants to be able to model how the alfalfas will grow in fields that are not in the experiment. Code. Results show that while pizza consumption and time are still significant main predictors, their interaction term did not reach significance. Repeated measures and split-plot models are special cases … pf (20.58, df1 = 2, df2 = 10, lower.tail = FALSE) ## [1] 0.0002853299. In contrast,random effects are parameters that are themselves randomvariables. Effects coding Simulating data, ---
title: "Chapter 17: Mixed Effects Modeling"
author: "Sushmita Shrikanth"
output:
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    theme: cerulean
    highlight: textmate
    fontsize: 8pt
    toc: true
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---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = FALSE)
```

# Background Information
Mixed models are especially useful when working with a within-subjects design because it works around the ANOVA assumption that data points are independent of  one another. In a within subjects design, one participant provides multiple data points and those data will correlate with one another because they come from the same participant. Therefore, using a mixed model allows you to systematically account for item-level variability (within subjects) and subject-level variability (within groups).

**When to Use?** -- Studies that obtain multiple measurements over time (longitudinal, time-series) or multiple trials per participant (within subjects) lend themselves well to mixed model analyses.

The following example will illustrate the logic behind mixed effects models.

## Example: National Pizza Study
Let's say that we are interested in examining the effect of pizza consumption on people's moods. Each participant provided an average number of pizzas consumed, and measurements are collected at 15 timepoints 

- Hypothetical sample size, **n = 30**
- **DV**: Mood rating (scale)
- **IV1**: Pizza consumption 
- **IV2**: Time points (Weeks, 1-10)

Here is some hypothetical data (code used to generate data can be found [here](https://github.com/RInterested/SIMULATIONS_and_PROOFS/blob/master/Athletes%20mixed%20effects)): 

```{r include = FALSE}

rm(list = ls())
set.seed(0)
library(lme4)
library(mvtnorm)

subjects = 30
time = 10
 
i = 0.2 
s = 0.5 
r = 0.5
cov.matrix1<-  matrix(c(i^2, r * i * s, r * i * s, s^2), nrow = 2, byrow = T)

require(mvtnorm)
random.effects_subjects <-  rmvnorm(subjects, mean = c(0, 0), sigma = cov.matrix1)
subjects.df = data.frame(subject  = c(1:subjects)) 
subjects.df$alpha_subjects = 1 + random.effects_subjects[, 1]
subjects.df$beta_subjects =  2 + random.effects_subjects[, 2]

i =   0.8   
s =   0.2 
r = -0.01   
(cov.matrix2 <-  matrix(c(i^2, r * i * s, r * i * s, s^2), nrow = 2, byrow = T))

random.effects_time <-  rmvnorm(time, mean = c(0, 0), sigma = cov.matrix2)

time.df = data.frame(time  = c(1:time)) 
time.df$alpha_time   =    -1 + random.effects_time[, 1]
time.df$beta_time    =     1 + random.effects_time[, 2]
summary(time.df$beta_time) 
sd(time.df$beta_time)     
summary(time.df$alpha_time)
sd(time.df$alpha_time)
cor(time.df$alpha_time, time.df$beta_time) 

observations <- subjects * time
observations.df <-  data.frame(
  subject = sort(rep(c(1:subjects), time)),
  time = rep(c(1:time), subjects), 
  pizza = rep(rnorm(subjects * time, 30, 5)))
dat1   <-  merge(subjects.df, observations.df)
dat2   <-  merge(dat1, time.df)
dat3   <-  dat2[with(dat2, order(subject,time)), ]
rownames(dat3)   <-  1:nrow(dat3)


df <-  within(dat3, 
              mood <-  alpha_subjects + pizza * beta_subjects +
                alpha_time    + pizza * beta_time    +
                0.75 * rnorm(n = observations)) 

head(df)
pizzadata <- df[,-c(3,4,6,7)]
```


```{r echo = FALSE}
head(pizzadata)

```

**NOTE** - This is a within-subjects study. All participants are providing multiple measurements. 

## Important Terminology 
Below are some important terms to know for understanding the statistical concepts used in mixed models:

###Crossed & Nested Designs
**Crossed designs** refer to the *within-subject* variables (i.e. timepoint, condition, etc.). Crossed designs occur when multiple measurements are associated with multiple grouping variables. In a completely crossed design, all subjects provide responses for all conditions/time-points.

  - Pizza study: We have subjects providing responses at 10 time points. Thus, we have a crossed design. 
  
**Nested designs** refer to the *between-subject* variable. Generally this is a higher-level variable that subjects or items are grouped under.
  
  - Pizza study: Not nested.

###Fixed v. Random Effects
**Fixed effects** are, essentially, your predictor variables. This is the effect you are interested in after accounting for random variability (hence, fixed). 
 
  - Pizza study: The fixed effects are PIZZA consumption and TIME, because we're interested in the effect of pizza consumption on MOOD, and if this effect varies over TIME. 
  
**Random effects** are best defined as noise in your data. These are effects that arise from uncontrollable variability within the sample. *Subject* level variability is often a random effect.
 
  - Pizza study: Controlling for random effects of subject, pizza consumption, and effect of time on subject, all of which vary across participants. 

**NOTE** - Predictor variables can be both fixed (i.e. causing a main effect/interaction) and random (i.e. causing variance/variability in responses). When building your models, you can treat your predictor as a fixed & random factor. 

### Slopes v. Intercepts: 
To better understand slopes and intercepts it maybe helpful to imagine plotting the relationship between the IVs and DV for each subject.

**Intercepts**: The baseline relationship between IV & DV. Fixed effects are plotted as intercepts to reflect the baseline level of your DV.
  
  -	Random intercepts: Variability in baseline measurements 
      
      * Pizza Study: Different baseline levels of pizza consumption across subjects
      
  - Fixed intercepts: Baseline variance is not affected
  
      * Pizza study: 

**Slope**: The strength of the relationship between IV & DV (controlling for randomness), which represent random effects. You should expect to see differences in the slopes of your random factors. 
  
  - Pizza study: The strength of the relationship between pizza consumption and mood will vary from person to person, resulting in random slopes per subject. Because subjects start at  

**Note**: If 2 variables share a lot of variance, the random intercepts and slopes may be correlated with one another. This can be accounted for in random structures as well. 

**Hypotheses For Study**
Random effects: 
- "Subjects" will have their own intercepts. 
- Subjects' slope will vary by pizza consumption intercepts, and by timepoint intercepts. 
- The slopes and intercepts of pizza consumption and time will be correlated (shared variance)
Fixed effects: 
- Expecting there to be an overall main effect of pizza consumption over time. 
- Expecting interaction such that more pizza over time predicts mood. 

# Setting up data in R 
- **Coding**: Recode your variable (mean-centered, effects) as best suited for your data. 
- **Long Format** : Refer to [TidyR chapter](http://ademos.people.uic.edu/Chapter9.html) 
- **Packages**: Make sure you have the following packages downloaded: 

``` {r, message=FALSE, echo=TRUE}

library (lmerTest) # Mixed model package by Douglas Bates, comes w/ pvalues! 
library (texreg) #Helps us make tables of the mixed models
library (afex) # Easy ANOVA package to compare model fits
library (plyr) # Data manipulator package
library (ggplot2) # GGplot package for visualizing data

```


#Modeling Procedure
Modeling conventions differ by field, but this example will begin by fitting the null model first, then building up hierarchically.
 

## Random effects structure
The *null model* will be fit to the [maximal likelihood estimate](http://lme4.r-forge.r-project.org/lMMwR/lrgprt.pdf). The random effects structure reflects YOUR understanding of where to expect variance, and how nested data will interact with that variance. The general syntax is as follows:

``` 
(1 + IV | unit level)  
(1 + IV.1*IV.2 | unit level)

#or

(0 + IV | unit level)
(0 + IV.1*IV.2 | unit level)

```
When there is a 1 before the line, you are accounting for random intercepts (varying baseline levels) in your variable. A O indicates the variable has a fixed intercept and not a random one.  These are a few hypothetical random effects structures:

  - ```(1| subject)``` = Random intercepts and slopes for subjects (different baselines, different average effect per subject).
  - ```(1 + pizza |subject)``` = The effect of pizza will vary *between* subjects. Random intercepts for pizza consumption, random slopes
for subjects influenced by pizza consumption. 
  - ``` (1 + pizza | subject) + (0 + time| subject)``` = Subjects have random intercepts and slopes as influenced by pizza consumption. Time slopes can vary as function of the subject, but variance between pizza consumption and time as independent
  - ``` (1 + pizza + time | subject)``` = Same as above, but variance between pizza consumption and time are SHARED (pizza consumption has relationship with time that varies by subject). 
  - ``` (1 + pizza * time | subject)`` =  Each subject can have their intercept, random slopes influenced by pizza and time, and their interaction between pizza and time. IMPORTANTLY, all random slopes and intercepts can be *correlated*. 
  
### Fitting Best Random Effects Structure
The ```lmer``` package can be used for modeling, and the general syntax is as follows: 
 ```
 modelname <- lmer (dv ~ 1 + IV +(randomeffects), data = data.name, REML = FALSE)
 
 ```

You can name each model whatever you want, but note that the name of the dataframe containing your data is specified in each model. Keep ``` REML = FALSE ```. 

First, however, we need to specify the random effects term that best fits the data. Try out different structures, and use the ```anova``` function to find the best fitting random effects structure. This function compares the fit of the model to see how fit has improved with additional items. You can also **visualize your data** to see what fits. ### Insert ggplot2 reference.  

``` {r echo = TRUE, message = FALSE}
nullmodel1 <- lmer( mood ~ 1 + (1|subject), data = pizzadata, REML=FALSE)
nullmodel2 <- lmer( mood ~ 1 + (1 + pizza |subject), data = pizzadata, REML=FALSE)
nullmodel3 <- lmer( mood ~ 1 + (1 + pizza * time |subject), data = pizzadata, REML=FALSE)

anova (nullmodel1, nullmodel2, nullmodel3)
```

Refer to the p-values in the output to see whether there was an improvement in fit. Because there was an improvement in between model 1 and model 2, but NO improvement between model 2 and model 3, we can proceed using the best fit model, `nullmodel2`, as our random effects structure for the rest of the analyses. 

## Fixed effects
Specific predictors can now be introduced into our model by specifying the DV followed by the predictor, random effects, and the dataframe. 

**Model 1** - Pizza consumption predict mood (main effect): 

```{r echo = TRUE, message = FALSE, error = FALSE}
m1=lmer(mood ~ pizza + (1 + pizza + time |subject), data=pizzadata, REML = FALSE)
summary(m1)

```

This model appears to show pizza consumption as a positive predictor of mood, as indicated by a posi

Random effects: 

  - SD reflects the amount of variation. Check correlation between intercept and slope (i.e. if intercept increases, slope increases). 
    
Fixed effects

  - Check estimates for beta value -- time has a significant effect, improvement in mood by about 1 point over time. 
  - Check correlation of fixed effects -- if too high, this may imply [multicollinearity](http://ademos.people.uic.edu/Chapter13.html)

**Model 2** -- Pizza consumption and timepoints included as predictors of mood. 
```{r echo = TRUE, message = FALSE, error = FALSE}
m2= lmer(mood ~ pizza + time + (1 + pizza + time |subject), data=pizzadata, REML = FALSE)
summary(m2)

```

```{r echo = TRUE, message = FALSE, error = FALSE}
m2= lmer(mood ~ pizza + time + (1 + pizza + time |subject), data=pizzadata, REML = FALSE)
summary(m2)

```

Results show significant effects of both pizza consumption and time on mood! Do they interact? 

**Model 3** -- Including an interaction term between pizza consumption and time (pizza consumption varies over time)

```{r echo = TRUE, message = FALSE, error = FALSE}
m3 = lmer(mood ~ pizza*time + (1 + pizza + time |subject), data=pizzadata, REML = FALSE)
summary(m3)

```

Results show that while pizza consumption and time are still significant main predictors, their interaction term did not reach significance. 

## Comparing Model Fit 
The ANOVA function allows you to compute Chi-squares between each model to see the improvement in model fit. The `effects` package should also include p-values in the output. 

```{r echo = TRUE}

anova (m1, m2, m3)

```

As you can see by the p-values, while there is an improvement in fit from model 1 to model 2, model 3 did not explain more variance. As such, model 2 appears to be the best fit.

We can now conclude that after controlling for random effects, more pizza consumption does lead to improvements in mood over time, but there is no interaction with time. 

This concludes the tutorial on mixed effects models. Below are references for additional information 
# References 
[Checking assumptions](http://ademos.people.uic.edu/Chapter18.html)
[More theory here](http://www.stat.cmu.edu/~hseltman/309/Book/chapter15.pdf), [here](http://jakewestfall.org/misc/BDB2008.pdf), and [here](http://www.bodowinter.com/tutorial/bw_LME_tutorial2.pdf).
[Effects coding](http://www.martijnwieling.nl/R/sheets.pdf)
[Simulating data](http://anythingbutrbitrary.blogspot.in/2012/10/hierarchical-linear-models-and-lmer.html)

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